A youth product of Grasshoppers, Rhyner made his professional debut with his childhood team in a 2–0 2016–17 UEFA Europa League qualifying phase and play-off round loss to Fenerbahçe on 25 August 2016. He debuted for Grasshoppers in the Swiss Challenge League in a 4–0 loss to on 23 October 2016. On 30 January 2017, Rhyner was loaned out to Schaffhausen to gain first-team experience in the Swiss Challenge League.
On 8 January 2018, Rhyner returned to Grasshoppers after a successful year with Schaffhausen.
On 10 July 2019, Rhyner moved abroad and joined Spanish Segunda División side Cádiz CF on a three-year deal. On 5 October of the following year, after featuring rarely as his side achieved promotion to La Liga, he moved to FC Cartagena in the second division, on loan for one year.